Question

the sum of digit of a two digit number is 9 when we interchanging the digits it is found that the resulting new number is greater than original number by 27 what is the two digit number

Answer 1

ATQ
x + y = 9
original no. = 10x+y
after interchange =10y+x
then
10y+x=10x+y+27
9y-9x=27
9(y-x) = 27
y-x=3
by eliminating method
2y=12
y = 6
putting value of y in eqn 1
x+6=9
x=3
hence the no. is 39

Answer 2

Answer:

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Given

The sum of the two digits = 9

On interchanging the digits, the resulting new number is greater than the original number by 27.

Let us assume the digit of units place = x

Then the digit of tens place will be = (9 – x)

Thus the two-digit number is 10(9 – x) + x

Let us reverse the digit

the number becomes 10x + (9 – x)

As per the given condition

10x + (9 – x) = 10(9 – x) + x + 27

⇒ 9x + 9 = 90 – 10x + x + 27

⇒ 9x + 9 = 117 – 9x

On rearranging the terms we get,

⇒ 18x = 108

⇒ x = 6

So the digit in units place = 6

Digit in tens place is

⇒ 9 – x

⇒ 9 – 6

⇒ 3

Hence the number is 36